In such case, that you want to enjoy the privacy and comfort of a passenger car, do not hesitate to use the normal coloured Taxi marked Taxi Meter. For the majority of taxi drivers that will be a deal of the day, and therefore, they will be happy to make a deal with you. But beware! Price must be arranged in advance! The usual and acceptable price will be somewhere around 3.300 – 3.500 Baht including ferry. But definitely do not pay more than 4.000 Baht and feel free to take another taxi in such case the driver will ask for more then 4.000 Baht. There are thousands of Taxis especialy in Bangkok and you do not need to take the first one.
One important information about taxi services and airport: Public taxis which are truly the most convenient and safe, are only available in the lowest floor of the Suvarnabhumi airport building. I do not recommend anyone to accept the offer in the arrivals hall at all! What they will offer you is prices about 700 – 1.400 Baht for a taxi from the airport to central Bangkok, which is the distance around something like 20 km, and that is price several times more expensive then you can really get. Remember, that the price per km for normal taxi is around 5 Baht and the starting rate is 35 Baht per trip, so normal taxi to central Bangkok will cost you as low as around 150 Baht!!! Do not, therefore, take brutally overpriced taxi offers in the arrivals hall and continue walking to the lowermost floor, where public taxis are. And later, anytime you will be using public taxi in Bangkok, always insist to use taximeter and never approach the offer of the taxi driver for a lump sum price. Be sure, that using taximeter will always be the cheapest!